# Detect signals degree of imbalance

I have got this question: let's suppose that I have three signals, representative of the same variable, but taken on three different component of a same device; in my case, three load signals, representative of the out-of-plane bending moment Mx of each of the blade of a wind turbine.

Is it any possible to effectively and efficiently detect the degree of imbalance or asymmetry of such signals?

With asymmetry and imbalance I mean a single parameter/variable which gives information about how the three signals differ from each other.

I would then set-up a threshold value to this degree of difference, in order to further trigger a certain process when the threshold has been overcome.

The first idea I came up with is multiple correlation, but perhaps there exist tons of better methods.

EDIT

1. Each signal coming from each blade;
2. Blades placed with 120 deg phase shift;
3. Azimuth angle vs. Time available.
4. Regarding balance vs. unbalanced, I only know that unbalanced condition leads to higher loads on blades. In general, the three signals will always be unbalanced: what I would like to ascertain is the degree of imbalance; is it over a defined allowed limit or not?
• Sometimes it makes sense to use something about the geometry of the problem. Is each signal from each of the three different blades? And are the blades at 120 degrees to each other? Do you have knowledge (or data) for what a balanced sequence of measurements looks like versus what an unbalanced sequence looks like? Do you have access to the angle of rotation vs time, too? – Peter K. Oct 12 '13 at 21:07
• @PeterK.: I just edited the post. – fpe Oct 13 '13 at 16:35

One thing that can be useful in condition monitoring of rotating machines when rotation angle is important is to look at using circular or directional statistics.

Suppose your measurements are: $$m_1(n), m_2(n), m_3(n)$$ for the three moments $m_i(n)$ for $i=1,2,3$.

Calculate the instantaneous directional mean of the moments: $$m_{\rm tot}(n) = \left ( m_1(n) + m_2(n) e^{j2\pi/3} + m_3(n) e^{j4\pi/3} \right)\\ \bar{\phi}(n) = \arg \left( m_{\rm tot}(n) \right)$$ assuming that the first blade is your reference.

This direction, $\bar{\phi}$, is the direction of the average moment. If it's always aligned (or "anti-aligned") with one particular blade of your turbine, then that can indicate your "problem blade".

You can use the magnitude $$\left| m_{\rm tot} \right|$$ as a measure of how "out of balance" the turbine is, as this should be (close to) zero most of the time.

If you have the azimuth angle, $\theta$, then you can get fancier. It may be that you need to angle-align (rather than time-align) your measurements to pick the faulty blade.

• I think this will be quite a useful suggestion: I will definitively give it a try. Are there other possible alternative that you know? – fpe Oct 15 '13 at 13:17
• The main other option is as I suggest at the bottom: resample the moments based on azimuth rather than time. That way, you can compare each blade's moment "distribution" in azimuth with the "average" blade moment "distribution" using the circular / directional analog of variance. – Peter K. Oct 15 '13 at 13:19